Political, philosophical, and theological reflections from a Christian idealist with libertarian leanings and a professional interest in science and mathematics.

Sunday, June 26, 2011

From mathematics to theology

[T]heology is, for all its modesty, in an exemplary way a free science. This means it is a science which joyfully respects the mystery of the freedom of its object and which, in turn, is again and again freed by its object from any dependence on subordinate presuppositions.

--Karl Barth, Evangelical Theology: An Introduction

In modern usage, science is the study of a particular object or range of objects. Physics takes as its objects the most basic or "fundamental" objects of the empirical world, e.g. particles, energy, forces. Biology takes as its objects all living things, though it is not at all times clear what this means. Economics may take as its object particular markets, e.g. the housing market or the automobile industry, or it may take that grand object which Hayek liked to call the "catallaxy." In all cases, the amount of knowledge we can obtain about something is often inversely proportional to the level of complexity with which we are dealing. This is how it is usually described: physics studies the most simple objects, chemistry studies one level of complexity higher (i.e. compounds of the most basic materials), biology studies another level, psychology and neuroscience perhaps another level higher, environmental science and ecology another level still, and finally the social sciences: sociology, economics, and political science.

If we can classify mathematics as a science, it precedes even physics on this staircase of complexity. As John von Neumann said, "If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is." Mathematicians study the very simplest objects of all: those which can be defined precisely and axiomatically, and which therefore can be understood with absolute certainty.
With different sciences now placed on a ladder of increasing complexity, it is then explained that the higher you go up the ladder, the less and less certain you are about what you infer from study. For instance, we are much less certain about economic theory (and therefore succumb to many more debates on the subject) than we are about physics. Newtonian mechanics may have been technically subsumed by Einstein's theory of general relativity, and yet we really have very little need to question Newton in everyday engineering problems. And if Einstein's theory ever gets corrected in any significant way, this, too, will not cause too much personal anxiety for committed physicists. The same cannot be said for economists, who are constantly debating (even bickering) about the proper interpretation of the same data.

But still, I imagine the ladder is probably somewhat misleading. Is human civilization really more complex than the ecosystems in which we live? A moment's reflection suggests this is doubtful. Certainly it seems strange to suggest that human psychology is inherently more complex than all other kinds of biological systems. And yet I wouldn't want to let go to the order in which I have placed the various sciences. It just appears complexity isn't the criterion I'm after.

No, the concept I'm really after is freedom. Why? Because science progresses through its ability to control an object. This is, in fact, explicit in all scientific work published today. What are the controls? What are the variables being isolated? The entire scientific method appears to be built on the basic philosophy that (i) all of reality operates according to certain unbending rules, and (ii) certain parts of reality can be controlled, isolated from one another, and made to reveal which rules govern their relationship with other parts of reality. And this seems to work pretty well, until you climb higher and higher up the ladder.

A human being is not necessarily more complex than other organisms. A human is, however, less controllable. This is precisely the trouble with psychology and even neuroscience. It's just so hard to control enough of the variables present when interacting with human beings. On the other hand, we can put rats into cages and cultures of bacteria into petri dishes. The amount of control we have over other organisms means we can gain more scientific understanding of them. Inorganic compounds are even easier to control. Basic particles and forces are the easiest of all: one need not doubt, for instance, that protons and electrons attract and all massive objects have gravitational fields. I do not use "easy" here to mean that it costs no money to run experiments or requires no sophisticated equipment--far from it. I simply mean that physicists are, almost by definition, the scientists charged with studying those parts of the world in which it is easiest to identify and isolate variables.

Again, if we are including mathematics in this scale, then it precedes even physics. The objects of mathematics are more controlled than any empirical object. They are defined axiomatically, and the relationships between them are absolute. They have no freedom whatsoever. Hence von Neumann's statement. Mathematics is "simple" because we control it. It operates according to our definitions and our logic. Living things--especially human beings--possess far too much freedom to come under such a precise study as mathematics. Thus certainly psychology and probably biology will never possess absolute mathematical precision. The world is not so controllable.

As a brief aside, when we see mathematics invading every realm of study, from chemistry and biology on up through economics and sociology, we can be assured that humans are trying to gain more control over their world. There is a certain level of presumption that goes with this. I am convinced that mathematical economics, despite whatever it can tell us, cannot solve the fundamental problems of economics, and mathematics in sociology may well be the worst idea ever conceived. When human beings come to be seen merely as numbers--even as random variables (which are just distributions of numbers)--then the notion of human volition has been demolished. This can only distort our understanding of the world.

Now, what have we not mentioned? The title of this post is, "From mathematics to theology." If mathematics is the most precise science because its objects are under the most exact control, theology must necessarily be the least precise, because its object is the least controllable. If it is pretentious to think we can control human beings, how much more outrageous to think we can control God! And yet control is the path to scientific knowledge as we know it. There must be very little, then, that we can scientifically know about God.

Indeed, I view mathematics and theology as more than mere ends of the spectrum; they are absolute polar opposites. No science could ever exist outside these poles. On one end, mathematics studies objects in the absolute most controlled setting possible: the setting of pure invention and pure abstraction. All mathematical objects are products of the human mind, and by design they can never change from what we declare them to be. On the other end, theology studies the one object we can never have any control of whatsoever. Surely other human beings can be controlled to some extent. Surely there are patterns to human behavior which can be isolated by clever experimentation. Such can never be the case with God. As Barth said, theology is a free science, because it studies an absolutely free object.

However, mathematics and theology have both been studied under many illusions. On the one hand, the Platonists believe that mathematical objects are somehow empirically real, despite or even because of the fact that they are pure abstractions. On the other hand, many theologians (perhaps under the influence of Platonism, or who knows what kind of philosophy) are tempted to think that God can be understood abstractly and precisely. Thus we worship the abstract principles of our own making. Thus we commit the most highly sophisticated of all idolatry: the worship of our own disembodied creation.

To do mathematics under the Platonist illusion of realism is, perhaps, inconsequential and thus forgivable. To do theology under this illusion is, however, to wrap one end of the spectrum around to the other, thus closing the spectrum and making a circle, a circle of absolute human power over all the cosmos. All things are subject to our complete understanding, hence our complete control. Thus the human mind squeezes all the freedom--all the life--out of absolutely everything, until even God himself is dead, and we die with him.

The proper way to do science--the way which brings life--is to first respect the absolute freedom, and therefore the absolute incomprehensibility, of God. Second, we must respect also the freedom of the creation, which, while not absolute, is nevertheless real with respect to ourselves. In this we way achieve what Florensky called that "being-in-love with" creation, rather than merely the desire to control it.

The whole notion of "scientific determinism" (or any kind of "determinism") arises out of a limited human perspective. When we exert control over things, we see that they are forced to obey certain rules. Thus when we see that the world has certain discernible patterns, we somehow project a sense of "control" onto the whole of reality. And so fears that we are secretly being controlled and have no real freedom come up. Yet listen to what Florensky says:

"God cannot stop being God just as a triangle cannot make the sum of its angles unequal to 180 degrees." [Spinoza] By contrast, the Christian idea of God as Essential Love, as Love inside Himself, and therefore also outside Himself; the idea of God's humility, of His self-abasement, manifested first in the creation of the world, i.e., in the placing of autonomous being alongside Himself, in the gift to this being of the freedom to develop according to its own laws, and therefore in the voluntary limitation of Himself--this idea for the first tiem made it possible to recognize creation as autonomous and therefore morally responsible to God. In the ancient world, there could be no idea of the moral responsibility of creation to God, because there was no idea of the freedom of creation. Christ brought the idea of God's humility to its ultimate limit: God, entering into the world, casts off the image of his glory and puts on the image of His creation (see. Phil. 2:6-8). He subordinates himself to the laws of creaturely life. He does not violate the world order. Nor does He not strike the world with lightning or deafen it with thunder, as pagans though (recall the myth of Zeus and Semele). He only burns like a meek light before the world, drawing to Himself His sinful and weary creation, not punishing it, but calling it to wisdom. God loves His creation and is tormented for its sake, is tormented by its sin. God extends His arms toward His creation, implores it, calls it, awaits His prodigal son. And mankind, the head of creation, is responsible to God for creation, just as man is responsible for man.

The creation is free. We, too, are free. It is only our own presumption and corruption that threatens to destroy that freedom. It is only our own desire to control which threatens that freedom.

Science has caused much destruction because it has been done according to the wrong principle, namely the desire for control and for power. It ought to have been done always and only for the love of creation, including a sense of personal responsibility for its good use. Surely much of the blame goes to scientists themselves. But I say the most blame goes to the theologians and the philosophers, who killed God with their rationalism.

It is no wonder at all to me that Barth, who was a light shining in the darkness of the Nazi takeover, would also be the one who could say, "Theology is a free science." The heroes of the modern world are those who can stand up and courageously state that we are not in control. With control and determinism come oppression and evil. With freedom and responsibility come love and peace. It all begins with good theology, and good theology must be free, for it must respect the freedom of its subject. Then, too, might the other sciences respect the freedom of their subjects.

For as mathematics is the most precise of all the sciences, so it must also be applied with the greatest humility. I said before that mathematics in the social sciences may be the worst idea. Yet worse by far is mathematical theology. That is truly the road to serfdom.

No comments:

Post a Comment

Subscribe To

News Clips

My Blog List

About Me

I am a Christian who thinks that love is what the world needs. I am a mathematician who thinks that truth is worth seeking passionately. I like to read about current issues, like religion (and its relation to modern science), economics, education, abortion, and war. I don't have it all figured out, but writing about it helps me clarify my own thoughts. Socrates is one of my heroes.